Integrable discretisations for a class of nonlinear Schrödinger equations on Grassmann algebras
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Publication:397757
DOI10.1016/j.physleta.2013.10.018zbMath1293.35297arXiv1303.1853OpenAlexW1973263492WikidataQ59900662 ScholiaQ59900662MaRDI QIDQ397757
Georgi G. Grahovski, Alexander V. Mikhailov
Publication date: 12 August 2014
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1303.1853
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55)
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Cites Work
- Unnamed Item
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- Binary Darboux transformations in bidifferential calculus and integrable reductions of vacuum Einstein equations
- Integrable noncommutative sine-Gordon model
- Super-extensions of energy dependent Schrödinger operators
- Supersymmetric two-dimensional Toda lattice
- Lie algebras and equations of Korteweg-de Vries type
- A supersymmetric extension of the Kadomtsev-Petviashvili hierarchy
- A super soliton connection
- Theory of nonlinear lattices
- Lie superalgebraic approach to super Toda lattice and generalized super KdV equations
- The bi-Hamiltonian structure of fully supersymmetric Korteweg-de Vries systems
- Inverse-scattering problem for a system of differential equations
- Integrable evolution equations on associative algebras
- Nonlinear chains and Painlevé equations
- Towards noncommutative integrable systems
- Quasideterminants
- An integrable noncommutative version of the sine-Gordon system
- A fully supersymmetric AKNS theory
- Towards the construction of \(N=2\) supersymmetric integrable hierarchies
- New integrable lattice hierarchies
- Nonlinear superposition principle for the Jordan NLS equation
- The extended supersymmetrization of the nonlinear Schrödinger equation
- Darboux transformations, finite reduction groups and related Yang–Baxter maps
- Cosymmetries and Nijenhuis recursion operators for difference equations
- Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
- Algebraic construction of the Darboux matrix revisited
- Supersymmetric extension of the Korteweg–de Vries equation
- Nonlinear differential difference equations as Backlund transformations
- Bäcklund transformation solutions of the Toda lattice equation
- Non-abelian integrable systems of the derivative nonlinear Schrödinger type
- Solutions of matrix NLS systems and their discretizations: a unified treatment
- Yang–Baxter maps and multi-field integrable lattice equations
- An algebraic scheme associated with the non-commutative KP hierarchy and some of its extensions
- A supersymmetric extension of the Toda lattice hierarchy
